What is the Least Common Multiple of 67 and 78?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 67 and 78 is 5226.
LCM(67,78) = 5226
Least Common Multiple of 67 and 78 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67 and 78, than apply into the LCM equation.
GCF(67,78) = 1
LCM(67,78) = ( 67 × 78) / 1
LCM(67,78) = 5226 / 1
LCM(67,78) = 5226
Least Common Multiple (LCM) of 67 and 78 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 78. First we will calculate the prime factors of 67 and 78.
Prime Factorization of 67
Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:
67 = 671
Prime Factorization of 78
Prime factors of 78 are 2, 3, 13. Prime factorization of 78 in exponential form is:
78 = 21 × 31 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 78.
LCM(67,78) = 671 × 21 × 31 × 131
LCM(67,78) = 5226